21 Triangles - 22 circles - 23 trig

Question 1

confusing concept

for any triangle, the sum of any two sides must be

Answer 1

greater than the third

Question 2

technique

the golden rule of geometry problem is

Answer 2

to draw a picture

Question 3

key formula

Pythagorean theorem

Answer 3

a^2 + b^2 = c^2

Question 4

key formula

common triples right triangles:

Answer 4

3-4-5
6-8-10
5-12-13
7-24-25
8-15-17

Question 5

key formula

special right triangles

Answer 5

45-45-90
30-60-90

Question 6

key formula

45-45-90

Answer 6

x^2 + x^2 = (x√2)^2

Question 7

key formula

30-60-90

Answer 7

x^2 + (x√3)^2 = (2x)^2

Question 8

confusing concept

when two triangles have the same angles measures

Answer 8

their sides are proportional

Question 9

key formula

π radians =

Answer 9

180 degrees

Question 10

key formula

area of a circle

Answer 10

πr^2

Question 11

key formula

circumference of a circle

Answer 11

2πr

Question 12

key formula

arc length

Answer 12

2 π r (θ/360°)

Question 13

key formula

area of a sector

Answer 13

πr^2 (θ/360°)

Question 14

confusing concept

central angles have the same measure as

Answer 14

the arcs that they “carve out”

Question 15

confusing concept

inscribed angles are half the measure of

Answer 15

arcs that they “carve out”

Question 16

key formula

angles inscribed in a semicircle are always

Answer 16

90 degrees

Question 17

confusing concept

a radius drawn to a line tangent to the circle is

Answer 17

perpendicular to that line

Question 18

key formula

general equation of a circle in the xy-plane

Answer 18

(x - h)^2 + (y - k)^2 = r^2,
where (h,k) is the center of the circle and r is the radius

Question 19

key formula

sin x

Answer 19

opposite/hypotenuse

Question 20

key formula

cos x

Answer 20

adjacent/hypotenuse

Question 21

key formula

tan x

Answer 21

opposite/adjacent

Question 22

confusing concept

trigonometric functions are

Answer 22

ratios

Question 23

confusing concept

sin 30 is always equal to

Answer 23

1/2
because all right triangles with a 30 degree angle are similar

Question 24

key formula

SOH-CAH-TOA

Answer 24

sin, cos, tan

Question 25

key formula

sin x =

Answer 25

cos (90 - x) or (π/2 - x)

Question 26

key formula

cos x in terms of sin equals

Answer 26

sin (90 - x) or (π/2 - x)

Question 27

confusing concept

signs of trig functions in quadrant I

Answer 27

sine, cosine, tangent are all POSITIVE

Question 28

confusing concept

signs of trig functions in quadrant II

Answer 28

ONLY sine is positive

Question 29

confusing concept

signs of trig functions in quadrant II

Answer 29

ONLY tangent is positive

Question 30

confusing concept

signs of trig functions in quadrant IV

Answer 30

ONLY cosine is positive

Question 31

key formula

ASTC

Answer 31

trig functions on the quadrants

Question 32

key formula

sin 0 =

Answer 32

0

Question 33

key formula

cos 0 =

Answer 33

1

Question 34

key formula

tan 0 =

Answer 34

0

Question 35

key formula

sin 90 =

Answer 35

1

Question 36

key formula

cos 90 =

Answer 36

0

Question 37

key formula

tan 90 =

Answer 37

undefined

Question 38

technique

to find the value of a trig function for an angle w/o a calculator

Answer 38

1. determine what the sign of the results should be (positive/negative)
2. find the reference angle
   e.g. if angle is 225, the reference angle is 225 - 180 = 45
3. use 45-45-90 or 30-60-90 special right triangles to get trig value for reference angle